AIAA 94-4510 The Effect of Robot Design on Force Control Performance with Implications for Micro-Gravity Applications M. Dohring and W. Newman Case Western Reserve University Cleveland, OH

AIAA Space Programs and Technologies Conference

September 27-29, 1994 / Huntsville, AL For permission to copy or republish, contact the American institute of Aeronautlcs and Astronautics 370 L'Enfant Promenade, S.W., Washington, D.C. 20024

AIAA-94-4510

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THE EFFECT OF ROBOT DESIGN ON FORCE CONTROL PERFORMANCE WITH IMPLICATIONS FOR MICRO-GRAVITY

APPLICATIONS* Mark Dohringtand Wyatt Newmanr

Case Western Reserve University Cleveland, Ohio

Abstract This paper presents experimental work performed on a robot with harmonic-drive transmissions to achieve high-performance position and force control. This work investigates the effects of sensor and actuator colloca- tion influences on compensating nonlinear transmission effects. I t is shown how proper combination of proxi- mal and distal sensor signals in feedback can result in dramatic improvements in both positioning accuracy and force regulation. Data is presented demonstrating an order of magnitude performance improvement using combined proximal and distal sensors, vs proximal or distal sensors alone.

1 Introduction There has been much interest in the use of robotic sys- tems in micro gravity environments. In addition to the usual requirements of compact size and low mass for mechanisms for space applications, mechanisms for micro gravity applications must also minimize the ac- celerations they induce on both the object being ma- nipulated and the spacecraft. This not only requires very slow manipulation, but it also requires “smooth- ness”. The effects of transmission ripple, Coulomb fric- tion, and other non-linearities can induce accelerations of several milli-G’s on the manipulated object [l].

Robot systems for micro-gravity applications must be designed to minimize jerky motions. The question is what are the design guidelines for “smoothness”? What are the most damaging disturbances, and how can they be overcome, either by mechanical design

*Copyright 01994 by Mark E. Dohring and Wyatt S. New- man. Published by the American Institute of Aeronaughtics and Astronautics, Inc. with permission.

!Graduate Student, Dept. of Electrical Engineering and Ap- plied Physics

t Associate Professor, Dept. of Electrical Engineering and Ap- plied Physics

or by control? Interestingly, using robots for high- performance force control imposes similar constraints on the mechanism’s characteristics. Much research has been done which shows that Coulomb frict,ion and transmission non-linearities can lead to poor sensitivity and contact instability. Much effort has been put into devising control methods that compensate for the un- desirable characteristics of the robot mechanisms (see, e.g., [Z, 3, 4, 5 , 6, 7, 8, 9, IO]). However, this research has suggested that there are ways to design the mecha- nism so that the task of compensation becomes easier. Sensor placement and transmission design are two im- portant factors affecting the controllability of undesired dynamics. The inertias of various components in the ~- drive train and of the manipulator it,self can act as me- chanical filters to reduce the effects of certain types of disturbance if they occur at the right locations relative to the sensors and actuators.

2 Sensor Placement

Using collocated sensors and actuators (which we shall call proximal sensing) is relatively easy to stabilize, but makes precise control of distal components difficult at best. The intervening dynamics create deviations from the ideal behavior. For example, in a robot po- sition control application, a tight PD control loop can be constructed using an encoder on the motor shaft. Even if this controller could be made to perfectly servo the motor to a desired angle, transmission compliance, transmission windup under load, and friction in drive components between the motor and the link it,self, will cause an error in the link position that cannot be cor- rected by the control feedback loop itself. Similarly, implicit force control [11] uses no external force sensing, but derives motor commands from the desired dynam- ics and physical displacement. If the manipulator were “ideal” the desired force would he precisely achieved. Direct-drive robots are actually fairly good at this type

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of control. However, in robots with large transmis- Traching Test Position Command

I sion ratios, large amounts of transmission friction and -Ox5 non-linear transmission dynamics seriously distort the

-0.7 end-effector forces which would result from the torques generated at the motors.

Proximal sensing alone, therefore, often can not achieve the desired performance. We must make use of more distal sensors to provide information about what the manipulator is doing. But what is the best way to do so? Can the distal sensors be used alone, or can and should proximal sensing be used in addition? Will the combination he better than either alone? This paper presents experiments designed t,o look into t,hese ques- tions in the realms of both position and force control.

yI

0 10 40 50 3 ExDerimental SetuD time: SBC

4

Experiments in position and torque control were con- ducted on a Robotics Research COID K2107HR robot

Figure 1: Approach Trajectory

[12, 131 This seven degree-of-freedom manipulator uses resolvers to sense joint positions and velocities and strain gauges to measure joint torques. The motors joint revolution.) drive the joints through harmonic drive transmissions

is a 16-bit device that also makes multiple turns per

and are 1ocat.ed at the joints themselves. Kinemati- cally, the robot is an alternatingseries of roll and pitch 4 Position Tests modules, with the pitch axes offset to provide griater range of motion of the pitch modules. This dexterity, combined with the over two-meter reach of the robot, produces a very large workspace.

The robob’s original control system has been retrofit to a custom multiprocessor system based on a VME backplane using Motorola 68020 based single-board computers [14]. The connec‘tion to the original con- troller, based on Intel’s Multibus I, is performed using a Bit3 bus to bus adapter. One of the control proces- sors in the RRC controller is used as a communcations server, collecting feedback information from the sensors and placing it, via the Bit3 adapter, into global mem- ory in the VME cage. A processor in the VME cage implements control servo loops on all joints with a loov raie of 1200 Ils. Other processors in-the VME system are used to collect data and generate joint trajectories. To test the effects of using proximal (motor shaft) vs. distal (transmission output) position and velocity sens- ing, joint four was retrofit with a 10,000-count incre- menral encoder connected directly to the motor shaft.. The encoder was interfaced directly to the VME system using a CAISR encoder interface card [15]. The en- coder’s resolution was similar to that of the resolver in counts/revolution ofjoint 4. The motor connects to the joint through a 100: 1 harmonic drive transmission, giv- ing 1,000,000 encoder counts per revolution vs. about 1,300,000 resolver counts per revolution. (The resolver i

Several experiments were conducted using various con- trol laws to control the position of joint 4 and mea- sure the resulting performance in a simple position- ing task. The remaining joints were controlled using resolver-based PD control. The control laws tried on joint 4 divide into three catagories: those using en- coder (proximal) feedback alone, those using resolver (distal) feedback alone, and those using both encoder and resolver feedback.

The positioning task selected for the experiments was an approach t o a goal position using sinusoidal trajectories. A plot of six and one quarter of these tra- jectories is shown in Figure 1 The position command followed the equation:

(1) Bd = + A f [1 - cos(2nft)l

during the excursion to more positive joint angles, lead- ing to,an approach toward the goal from “above”, and the equation:

(2) o d = 8, + A % [COS(2Tft) - 11

during the excursion to more negative joint angles, leading to an approach toward the goal from “below”. In these equations, fld is the current desired position, 0, is the final goal position, A is one-half the excursion, and f is the temporal frequency of the cosine For our

2

experiments, the motions were performed over a period

sion to allow the robot to settle. Desired velocities were generated from the derivatives of the position trajecto- ries. During the tests, the robot was posed such that link four could swing like a pendulum. The goal point for the approach trajectory was selected at the bottom

Several quantities were selected as performance mea- sures. Final positioning error, overall tracking error, “smoothness” as measured by the strain-gauge signal on joint 4. For our purposes, control was considered stable when it could converge near to the goal point and remain motionless with respect to the position feedback signal. This criterion was used to select the gains for the different control laws. The gains for each conbrol scheme were made as large as possible without produc- ing obvious vibration when a constant position com- mand was given. Vibration during motion was also kept as low as possible while still allowing reasonable gains.

trackhg error With respect to encoder of 2 seconds with a 2 second pause followingeach excur- b

,,5

: 2 o,5 % 5 24.5

? .1

.

of the swing to minimize any gravitational “droop”.

-2,5 0 10 20 30 40 50

11ms: SBC

Figure 2: Encoder P D control tracking error

anele shown in Fieure 3. Here the mean error when v Y

approaching from more positive joint angles (“above”) was 7.6 mrad. This may be attributable to encoder off- 4.1 Proximal P-D Encoder Feedback

~1~~ was used to perform a propor- set calibration for this case in which gravity load was tional+derivative (I’D) position control loop. minimized. However, data collected at higher gravity

load showed a 19 mrad droop. Clearly, accurate ab- solute joint positioning cannot he achieved with on a control law which depends solely on proximal feedback.

Tc = I<,,(@d - 8,) (3)

where T, is the torque command I<, is the position

I<u(Wd - W e )

gain I<, is the velocity gain, @d and wd are the desired position and velocity, and 0, and we are the encoder- derived position and velocity.

The tracking errors for several independent trials are shown concatenated together in Figure 2 . I<,, was 75,000 N-m / rad and IC, was 1,000 N-m / (rad/sec), with respect to the transmission output. For a second- order model with an estimated link inertia of 5kg-m2, these gains correspond to an undamped natural fre- quency of w, = 122 rad/sec and a damping factor of < = 1.6. The mean final positioning error with respect to the encoder was approximatly 0.1 millirad (mrad). The standard deviation of the strain gauge signal was chosen as a measure of the “smoothness” of the trajec- tory and found to be 10.1 N-tn for these runs. This is close to the 6.65 N-m “best” result obtained using en- coder feedback with much lower gains. The 6.65 N-m figure represents the effect of joint bearing friction and remains internal to the drivetrain, regardless of what control algorithm is used. The excess over this figure is a more accurate measure of vibration transmitted to the link.

The major drawback to encoder feedback, however is the large error generated with respect to the resolver

4.2 Distal P-D Resolver Feedback Much research has been directed toward the use of dis- tal feedback in linear control (see, e.g. [16, 17, 18, 19, 201 The problem is that these methods cannot handle modelling errors well, and do not respond well to highly non-linear transmission disturbances. Therefore, the great body of work developed in linear control theory is of limited use here.

Since the resolvers for the joints of the RRC arm are located at the output of the transmission, they pro- vide a precise measurement of actual joint positions. In principle, a PD feedback control law based on these distal sensors should be able to reduce the absolute position error. The control law is identical to that for encoder feedback except that, 0, and ur replace 8, and w e , respectively:

Tc = I ( P ( e d - 8 , ) + I < ” ( ( W d - W r ) (4)

Figure 4 shows the tracking error with respect to the resolver, for resolver PD control with ICp = 11,000 and IC, = 150. The equivalent second-order model pa- rameters are wli = 47 and < = 0.6. At these gains the -

3

J

sensed joint torque 200 I

J 10 20 30 40 50

time:sec

jl Figure 5: high gain resolver PD control strain gauge torque 10 20 30 40

time: s& .I lo

Figure 3: Encoder PD control resolver error vibration level was comparable t o the maximum-gain case of proximal PD control. maximum gains. Plac- ing the transmission inside the feedback loop made stabilizing bhe control far more difficult. The mean error for approaches from more negative joint angles (“below”) was 1.0 mrad, an order of magnitude worse than the encoder-based law could converge on its com- manded encoder position. Increasing the resolver gains to I(p = 25,000 and IC, = 350 t o acbicve higher ac- curacy led to greatly increased vibration, as shown in the plot of strain gauge torque in Figure 5 . With a standard deviation of 60 N-m, the vibrations are sig- nificant and would be transmitted both to the payload and through the base, which can be a serious drawback for precision operations in space. At higher gains, the distal feedback became unstable due to the unmodelled tranmission compliance.

4.3 Combined P-D Feedback Since neither the distal resolver nor the proximal en- coder could provide both high precision and smooth- ness yhen used alone in feedback, a strategy was sought to combine both signals in the control to improve the performance. One such approach is to use the resolver feedback to modify the desired position in the IC, term in equation 3 as in:

lime: h&

Figure 4: Resolver I’D control Resolver Error Te = I < p ( @ d , - 0,) + I ( v ( W d - W e ) (5)

where Bd, is chosen to be a function of Od and 0, such that the error ( B d - 8 , ) is driven to zero by the control

4

Seosed pint t0rq“B to, 1

J i o 20 30 40 50

-401 0

time: SEX

Figure 6: Z-paramet,er mixed proximal/distal feedback cont,roller

law. A straightforward choice is:

Bd, = 8 d + (0, - 8,) (6)

That is, the desired encoder position is equal to the de- sired joint poshion plus a correction based on the error between the encoder and resolver posit,ions. Subst,itut,- ing into 5 yields:

T = (ad - 0,) + I<uc (Wd - W e ) (7)

(The gains are now subscripted with their correspond- ing feedback source.) In this control law, the encoder is being used solely for velocity feedback while the re- solver is used for position. This two-parameter, mixed feedback PD control law was tested using maximum stable gains of K,,, = 25,000 and I{,,‘ = 1,500, pro- ducing a mean resolver error of 0 . G rnrad. The strain torqne signal, shown in Figure 6 , indicates that the vi- bration is significantly reduced to a standard deviation of 7.8 N-m, even though the resolver position gain was increased. This feedback law improved on the posit,ion accuracy over resolver feedback alone, and did so a t rel- atively low vibration. However, the accuracy achieved was still far from the potential suggest,ed by proximal feedhack.

One hinderance to better positioning is the limit on K P 7 . Thc non-linearities of the transmission get ampli- fied and lead to instability. For this reason, equation 6 was modified with a low-pass filter on the error term, giving:

(8) B d , = O d + L.P.F.(@, - 8,)

0 10 20 30 -3

#me: SBC

v

...............

.............

............ 4. ................

d 50

Figure 7: 3-parameter mixed proximal/distal fccdback controller tracking error

yielding a control law:

Tc = I(p.(Od-e,+L.P.F.(8,-8,))+I(,~(wd-w,) (9)

The approach experiment was performed by this con- trol law with ICp. = 75,000, IC,, = 1,000 and a cut,off frequency of 4 Hz.

The distal error correction compensator was a first- order low-pass filter. The corner frequency of 4 I lz was chosen to reduce thc distal gain from a maximum of 75,000 at low frequencies, t o a gain less than 25,000 a t frequencies shove 11 Hz. The critical frequency of 11 Ilz is near the link’s first resonance, though this freqnency varies with load, since the harmonic drive acts as a stiffening spring.

The tracking error for this controller, shown in Fig- lire 7, had a mean of 0.22 mrad when approaching from “below”, the more error-prone approach direc- tion. This nearly recovers the encoder angle accuracy of pure encoder feedback, but transfers this precision to the resolver. Further, the strain torque signal, shown in Figure 8, had a standard deviation of 10.5 N-m, nearly identical to the pure encoder case, showing thal i t is possible to combine the best features of both distal (ac- cnracy) and proximal (low vibration) feedback.

However, is this better than just using simplc PID control based on a distal sensor? To find out,, the exper- iments with resolver-only feedback were repeated with the addition of an integral m o r term, using the cont,rol law:

\-

./ rc = I ( p ( B d - O , ) + I ( , ( W d - W , ) + I ~ ;

5

40 .......I ..........; ................... j ........ ! .........

10 20 30 40 50 6 0 0

m e : sec

Mean Position Error

Figure 8: 3-parameter mixed proximal/distal feedback controller tracking error

Std. Dev. of Joint Toraue

Tracking error is shown in Figure 9 for gains of IC,, = 11,000, I<ur = 150, and I f i - = 50,000. The final posi- tioning error exhibited a wide range, seemingly getting "stuck" occasionally several milliradians away from the goal. However, in other trials, the integral term can be seen driving the error toward zero.

For comparison, the integral resolver term was addcd to the three-parameter mixed proximalldistal feedback controller giving a four-parameter mixed proximal/distal feedback controller:

TC =

J

(milliradians) Enc=O.l Res=7.6

Resolver=l .O

Tracking error and strain gauge torque are shown in Figures 10 and 11. Parameters were the same as with the thee-parameter controller, with the addition of If;r = 50000. Final positioning error averaged 0.05 mrad for approaches from more negative joint angles, and thc strain gauge torqiie standard deviation was 11 N-m.

The results are summarized in Table 1. (N-m)' 10.1 8.2 4.4 Position Feedback Conclusions

Our experiments on proximal and distal feedback on a system with significant nonlinearities have led to some important conclusions. It is not surprising that prox- imal feedback is much easier to stabilize than distal feedback. Higher gains, higher bandwidths, and lower tracking and sett,ling errors are obtainable with local

-./

.lo= tracking error 6, I

4 0 10 30 40 50

time: 5%

Figure 9: Resolver feedback PID controller

p o = tracking error

10 20 30 40 50 time: semnds

Figure 10: 4-parameter mixed proximal/distal feed- back controller tracking error

Control r- Proximal PD

lo gn. Distal PD hi gn. Distal P D Two-param. P D

Three-param. P D Distal PID I1 Four-param .PID

varied 0.050

Table 1: Position Control Results

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Figure 11: 4-parameter mixed proximal/distal feed- back cont,roller strain gauge torque

feedbackkat least with respect to local measurements. However, such local feedback fails to sense and cor- rect for distal errors. Feedback with respect to distal sensors alone is limited in bandwidth, and results in slower and limited-precision control. Advanced linear control kchniques can be exploited to better utilize distal sensors in linear systems. However, the distur- bances introduced by harmonic drives are, including Coulomb friction, load-dependent friction, tooth cog- ging, and load-dependent compliance, preclude the use of such linear feedback techniques.

Our best performance was obtained through a com- bination of proximal and distal sensor feedback. Prox- inial leedhack could he performed at high bandwidth, and distal feedback corrections could be introduced at a lower bandwidth. The bandwidth limitation for dis- tal fecdback was constrained by the first resonant frc- quency between the proximal and dist,al sensors.

5 Torque Control

The encouraging results of mixed proximal/distal feed- back for precise position control should have implica- tions for force control as well. It is well known that a scverely-limiting constraint on force feedback is inter- nal dynamics. In [21, 22, 231, simple 2-mass models are used to explain why endpoint force sensor signals, act- ing as distal sensors with respect to the actuator, are limited to low feedback gains. In [24], i t is shown why robots with quite low force-feedback gains, e.g. unity, oft,en exhibit contact instabilities when interacting with

stiff evironments. In order to achieve low-error force control it is nec-

essary to utilize endpoint force sensing. However, di- rect feedback of endpoint forces is limited to very low gains, resulting in poor performance. By analogy to PO- sition control, however, it can be shown that a mixture of proximal and distal feedback can result in superior performance.

In this section, we compare a purely “proximal” torque controller (implicit torque control) t o a distal torque-feedback controller. Neither controller has ac- ceptable performance. A third controller, called “Nat- ural Admittance Control”, utilizes proximal and distal sensors, and is shown to achieve dramatically better torque-control performance.

5.1 Experimental Procedure Utilizing the built-in joint-torque strain-gauge sensors in the RRC robot arm, we defined our henchmark task as achieving zero torque at transmission output ofjoint 4. Under various control algorithms, link 4 was manu- ally lifted, and permitted to fall into hard contact with a stiff surface. Joint torques were monitored during the fall, collision, and subsequent settling.

In addition, joint-4’s strain-gauge torque was moni- tored while the link was slowly lifted and lowered (man-

In all cases, the sensed joint torque ideally would have been zero. Any deviation from zero t,orque (except during the brief impact dynamics) is a measure of the tolerance of the controller performance.

L.‘

ually) by external forces. L

5.2 Implicit Torque Control Implicit torque control (or implicit force control), as described in [ll], is an attractive technique for low- friction systems. Implementation is simple, and the resulting system never exhibits contact instability. In this approach, one attempts to achieve a target output force/torque by exerting the kinematically-consistent torques on the actuators. For common electric drives, the actuator torque is linearly proportional to the drive current. In t,his method, proximal torques are inferred from drive currents, and to forccftorque sensors are needed.

In our henchmark torque-control comparison, the equivalent required motor torque was zero. Indeed, zero motor current (power off) results in zero clectro- magnetic torque induced on the motor rotor. In the absense of friction, our tests would have resulted in zero torqne observed at joint-4’s strain gauge.

Figure 12 shows the impact and int,eraction tests with joint 4’s motor off. The strain guage showed a ’~-

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Ume: JBC

Figure 12: Interaction with Implicit Torque Control: motor off

remanent joint torque of 2.9 N-m for the 16 drop tests, after impact dynamics decayed. Since the contact sur- face supported the weight of the link, the joint torque would have been ideally zero.

The interaction tests (from 43 seconds to GO seconds) consisted of inducing an external force on the link suffi- cient to move the joint slowly by approximately5 mrad. Over this excursion, one period of a signficant cogging torque could be felt, presumably due to tooth-to-tooth interactions in backdriving the harmonic drive trans- mission. The torque felt at joint 4 during this cogging transition had a standard deviation (rms amplitude) of 9.1 N-m, and peaks of approximately 15 N-m. Thus, it could be expected that an implicit torque controller would result in endpoint force errors as large as 15 N-m.

-'

5.3 Explicit Torque Control

Our next example controller utilized the strain-gauge joint-4 torque signal for feedback. The control law was:

Tcmd = fCr(7des - T a g ) (12)

where Tcmd is the torque commanded of the actuator, 7des is the desired joint torque, and rdg is the joint torque sensed by the strain gauge. The torque feed- back gain, ICt, was adjusted experimentally to deter- mine the maximum value which maintained stability in cases of stiff contact. The empirically-determined maximum gain was 0.3 (dimensionless loop gain).

For our benchmark test, the target joint torque, ?;les,

was zero As before, link 4 was subjected to both drop i

Figure 13: Interaction with Explicit Torque Control: Kt = 0.3

tests and interaction tests. The joint torque results for explicit torque control are shown in Fig 13.

The mean joint torque at rest on the table (after im- pact dynamics decayed) for the 14 drop tests was 1.3 N-m, an improvement over implicit torque control. For the interaction tests, the cogging torque was reduced to a standard deviation of 6.7 N-m. The cogging-torque reduction agrees well with the expected attenuation of 1/(1 + I C t ) for a gain of ICt = 0.3. Although the torque errors are reduced by a third, the result is hardly im- pressive. Attempts to achieve better control through higher feedback gains resulted in instability.

5.4 Natural Admittance Control

Finally, we present a force-control algorithm which combines utilization of proximal and distal sensors. The technique, called Natural Admittance Control, is described in experiments on other robot types in [25, 26, 4, 271.

The Natural Admittance Control (NAC) algorithm derives its name from a control policy which attempts to mimic the inate dynamics of a system, supplemented by desired stiffness and damping parameters, and pre- sumed devoid of friction. A high-bandwidth, proximal- feedback controller is constructed t o attempt to drive the system t o emulate this chosen set of desirable, yet feasible dynamics.

In the instance of our specific example, in which de- sired stiffness, desired damping and desired joint torque are all zero, Natural Admittance Control degenerates to the control law:

8

As can be seen in Fig 14, the NAC controller sharply reduced the joint-torque errors. The strain-gauge error a t rest on the contact surface was nearly zero-well be- low the noise level of the sensor. The strain-gauge rms noise level a t rest was approximately 0.5 N-m. From 31 seconds to 60 seconds. the interaction tests were ner-

\ -1

formed, with externally-induced slow link oscillations of approximatley one “cogging” period of 5 mrad. The cogging could hardly be felt by hand with this con- troller. During these tests, t+ strain-gauge torques in- creased by approximately 0’;3 N-m peak-to-peak. The

~~

rms strain-gauge torques~ indreased from a background noise level of 0.5 N-m to 0.75 N-m.

NAC achieved stable torque feedback w@g significantly attenuating force errors. Force errors under NAC were a factor of 50 lower than implicit force control (analagous to exclusively proximal feedback), and a factor of 35 lower than explicit force control (exclusively distal feedback).

Relative to implicit toSqdejcontrol, .\

time: SBC

Figure 14: Interaction with Natural Admittance Con- trol

i

7 m d = [l 7,gIJdT - we 3 (13)

In the control law above, J is the (estimated) link inertia, ~~g is the strain-gauge sensed joint torque, we is a proximal (encoder, in our case) velocity measure, Kne is a velocity feedback gain, with respect to the (proximal) encoder, and r,,d is the resulting actuator torque command.

Note that the NAC algorithm utilizes distal sensing (strain-gauge sensed torque) as a correction within a proximal (encoder velocity-based) feedback controller. Note, also, that the distal feedback must he bandwidth limited, according to some natural dynamic constraint of the system. In this case, the torque-sensor signal is limited by an integrator, which has high-frequency behavior identical to a first-order low-pass filter. In the case of position feedback, the low-pass filter pa- rameter of cut-off frequency was selected based on the system parameter of mechanical resonance. In the case of torque-sensor feedback, the integrator gain has units of inverse inertia. A “natural” choice for this gain is the use of the inherent link inertia. Empirically, such a choice of gain results in a stable system. Significantly larger integrator gains lead to contact instability.

Performance results of the NAG controller are shown in Fig 14. In this test, the integrator gain was set to 1 / J = 0.2 (in MKS units), based on our best estimate of link inertia. The proximal velocity feedback gain was set to Kve = 1,000, based on our empirical evaluations of stabilit,y limits of proximal velocity controllers.

6 Conclusion

Achieving smoothness is hard in the presence of transmission nonlinearities, friction, and other effects. Achieving other goals, such as precise positioning can lead to more vibration.

1 . Resolver feedback alone produces good final posi- tioning at higher gains , but must have fairly low gains for smoothness.

2. Encoder feedback alone remains quite smooth, even at fairly high gains. However, since the feedback is before the transmission, even a perfect position loop would lead to large absolute joint position errors.

3. Combining feedback from the encoder (for veloc- ity) and the resolver (for position) in an attempt to get the best of both worlds can improve final positioning while allowing higher damping factors.

Using encoder feedback for both position and velocity, and adding a low pass filtered version of the error between resolver and encoder positon produces better results.

5. Integral feedback can null out position errors, but is prone to limit cycling in the presence of friction.

6. Direct force feedback tends to be unstable a t useful gains. Feeding back a signal from a sensor closer to the motor is better, but still bas stability problems at higher gains. The torque gain had to be less than 1 to remain stable.

7. Natural Admittance Control permits distal feed- back as a correction signal to a proximal servo loop. NAC produced a large reduction in the apparent ma-

\-

4.

nipulator friction enabling higher torque sensitivity. -

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7 Acknowledgements J

Mark E. Dohring is supported by a NASA Space Grant/OAI Graduate Fellowship from the Ohio Space Grant Consortium

This work was also supported in part by NSF Young Investigator Award IRI-9257269 to Dr. Newman.

References [l] W. S. Newman, G. D. Glosser, J . H . Miller, and

D. Rohn, “The detrimental effect of friction on space microgravity robotics,” in Proceedings of In- ternational Conference on Robotics and Auloma- tion, (Nice, fiance), pp. 1436-1462, IEEE, May 1992.

p] W. S. Newman, G. D. Glosser, J . H. Miller, and D. Rohn, “The detrimental effect of friction on space microgravity robotics,” in Proceedings ofthe IEEE International Conference on Robotics and Automation, (Nice, France), pp. 1436-1462, IEEE, May, 1992.

[3] M. E. Dohring, E. Lee, and W. S. Newman, “A load-dependent transmission friction model: The- ory and experiments,” in Proceedings of the IEEE International Conference on Robotics and Au- tomation, (Atlanta, GA), pp. 3.430-3.436, IEEE, May 1993.

[4] W. S. Newman and Y. Zhang, “Stable interaction control and coulomb friction compensation using natural admittance control,” Journal o f Robotic Systems, vol. 11, no. 1, 1994.

[5] 3 . Tou and P. M. Schultheiss, “Static and sliding friction in feedback systems,” Journal of Applied

[9] T. Kubo, G. Anwar, and M. Tomizuka, “Appli- cation of nonlinear friction compensation to robot arm control,” in Proceedings of International Con- ference on Robotics and Aulomation, pp. 722-727, IEEE, 1986.

[lo] C. C. DeWit, P. Noel, A. Aubin, B. Brogliato, and P. Drevet, “Adaptive friction compensation in robot manipulators: Low-velocities,” in Pro- ceedings of International Conference on Robotics and Auto.mation, pp. 1352-1357, IEEE, 1989.

[ll] J. K . Salisbury, “Active stiffness control of a ma- nipulator in Cartesian coordinates,” in IEEE Con- ference on Decision and Control, pp. 95-100, 1980.

[12] W. S. Newman, M. E. Dohring, J . D. Farrell, P. H . Eismann, and H. I. Vold, “Preliminary work in impedance control on a kinematically redundant manipulator,” in Proceedings o f the Winter An- nual Meeting of the ASME, (New York), Dynamic Systems and Controls Division, American Society of Mechanical Engineers, 11-15 December 1989.

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